Answer:
∑E(x
) = 13.49167 floors
Explanation:
The expected number of floors no one get off = ∑E(x
) where i is from 0 to 23
and E(x
) = ∑x
P(x
)
here x
is the indicator of floor where no one gets off, its value is 0 when atleast one person get off on its floor and 1 when when no one gets off.
Now,
P(x
=1) = (22/23)¹²
P(x
=0) = [1-(22/23)¹²]
Now,
E(x
) = ∑x
P(x
) = 0* [1-(22/23)¹²] + 1*(22/23)¹² =0.586594704
For total number of floors where no one gets off
∑E(x
) = E(x₁)+E(x₂)+E(x₃)........................+E(x₂₃)
∑E(x
) = 23*0.586594704
∑E(x
) = 13.49167 floors